] calls Fuchsian equations. He has developed a rather general
theory of these equations. (See [105], [104], [103], and also the earlier papers [12], [106] and [107].) In [108] this was applied to analytic Gowdy spacetimes to construct a
family of vacuum spacetimes depending on the maximum number of
free functions (for the given symmetry class) whose singularities
can be described in detail. The symmetry assumed in that paper
requires the two-surfaces orthogonal to the group orbits to be
surface-forming (vanishing twist constants). In [97] a corresponding result was obtained for the class of vacuum
spacetimes with polarized
symmetry and non-vanishing twist.
A result of Anguige [6] is of a similar type but there are several significant differences. He considers perfect fluid spacetimes and can handle smooth data rather than only the analytic case. On the other hand he assumes plane symmetry, which is stronger than Gowdy symmetry.
Related work was done earlier in a somewhat simpler context by Moncrief [121] who showed the existence of a large class of analytic vacuum spacetimes with Cauchy horizons.
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Local and Global Existence Theorems for the Einstein
Equations
Alan D. Rendall http://www.livingreviews.org/lrr-2000-1 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |